CN110059379A - It is a kind of that Topology Optimization Method is combined with the compliant mechanism of APDL based on MATLAB - Google Patents
It is a kind of that Topology Optimization Method is combined with the compliant mechanism of APDL based on MATLAB Download PDFInfo
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- CN110059379A CN110059379A CN201910261554.XA CN201910261554A CN110059379A CN 110059379 A CN110059379 A CN 110059379A CN 201910261554 A CN201910261554 A CN 201910261554A CN 110059379 A CN110059379 A CN 110059379A
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- G06F30/20—Design optimisation, verification or simulation
- G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
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Abstract
The present invention is a kind of to combine Topology Optimization Method with the compliant mechanism of APDL based on MATLAB, by establishing the topological optimization model of compliant mechanism and the finite element analysis model of compliant mechanism, geometrical non-linearity calculating is carried out using finite element analysis software ANSYS, carries out topological optimization iterative process using numerical value software for calculation MATLAB.Complicated non linear finite element analysis part is given to professional finite element analysis software to complete, and gives numerical value calculating section to professional numerical software to calculate.The advantages of learning from other's strong points to offset one's weaknesses, each software is utilized to greatest extent, greatly improves computational efficiency, reduces programming difficulty, while ensure that the precision of solution.The present invention has many advantages, such as that versatile, easy to operate, computational efficiency is high.
Description
Technical field
The present invention relates to the field of structural design of compliant mechanism, in particular to a kind of flexible machine based on MATLAB and APDL
Structure combines Topology Optimization Method.
Background technique
Compliant mechanism, which refers to, utilizes the flexible deformation transmitting of material or the novel mechanism of converting motion, power or energy.It is flexible
The concept of mechanism is proposed by Buens equal to nineteen sixty-eight earliest, in subsequent more than 50 years, has been emerged largely about its basis
The research achievement of theoretical method.There are two ways to current more system and maturation, be that oblique mining method and topology are excellent respectively
Change method.
Oblique mining method is equal to 1994 by Howell earliest proposes that core ideas is: first by compliant mechanism approximation
Equivalent conversion is the rigid mechanism with torsional spring, then with the compliant mechanism that is needed of analysis and design method of rigid mechanism.
When designing lumped compliant mechanism using pseudo-rigid-body method, it is ensured that mechanism has good precision under small deformation, but deforms
When larger, due to pseudo-rigid-body method factor itself, even if defined movement can be completed, also inevitably make that structure is complicated, error compared with
Greatly.
Ananthasuresh of Univ Michigan-Ann Arbor USA in 1994 etc. for the first time draws the theoretical method of non-individual body topological optimization
Enter into the design of compliant mechanism, opens the new way of design compliant mechanism.Compared with pseudo-rigid-body method, using topological optimization
Method designs fatigue caused by when can deform brought stress collection neutralization component receiving cyclic loading to avoid mechanism local compliance
It destroys.
Large deformation output for compliant mechanism, due to the relationship in flexible deformation there are geometrical non-linearity, so that flexible
There is biggish difficulty in the design and application of mechanism, it usually needs are designed and analyze by finite element analysis software.In addition,
Compliant mechanism more complicated for structure is also essential using finite element software modeling.Since compliant mechanism occurs
There are GEOMETRICALLY NONLINEARs when flexible deformation, and non-linear side is often solved using Newton-Raphson method when calculating
Thus journey will generate huge calculation amount, or even the case where result does not restrain occurs.It is in number of patent application
In 201711438876.4 Chinese invention patent, it is excellent to propose a kind of topology that platform is solved based on MATLAB and CFX joint
Change method, this method are only applicable to flow field calculation, can not carry out statics Analysis.The present invention considers to use the side of combined optimization
Method solves complicated nonlinear problem by finite element analysis software ANSYS, simplifies programming difficulty, effectively improves computational efficiency.
Summary of the invention
Technical problems to be solved:
In order to avoid the shortcomings of the prior art, the present invention proposes a kind of compliant mechanism connection based on MATLAB and APDL
Topology Optimization Method is closed, in order to solve meter brought by the geometrical non-linearity generated during the output of compliant mechanism large elastic deformation
Difficulty problem is calculated, this method is considered to carry out geometrical non-linearity calculating using finite element analysis software ANSYS, be calculated using numerical value soft
Part MATLAB carries out topological optimization iterative process.
The technical scheme is that a kind of combine Topology Optimization Method with the compliant mechanism of APDL based on MATLAB,
Be characterized in that the following steps are included:
Step 1: the topological optimization model of compliant mechanism is established；Known target optimization region is defined as design domain Φ, benefit
It is with finite element analysis software that design domain Φ is discrete for n finite elements；Information after discrete includes that element number and node are sat
The element number and node coordinate are exported, and define x by markiFor the corresponding pseudo- density of i-th of discrete unit, viIt is i-th
The volume of discrete unit, with unit puppet density xiAs design variable；
With the minimum objective function of shared strain energy of the compliant mechanism, constraint condition is that the usage amount of material is less than body
The product upper limitThe objective function of optimization is as follows:
S.t.R (u, x)=0
0<xmin≤xi≤ 1, i=1,2 ..., n
Wherein, f is volume constraint score；The volume of V=1, V expression design domain Φ；Indicate the pact of design domain Φ volume
The beam upper limit；U is motion vector, and F is external applied load vector, FTFor the transposition of external applied load vector, R is global Unbalanced force vector, and C is
The shared strain energy function of outgoing mechanism；
Step 2: the finite element analysis model of compliant mechanism is established；The element number after will be discrete in step 1 and
Node coordinate correspond, and using parametric programming language APDL write it is discrete after as a result, realize it is soft in finite element analysis
Finite element analysis model is constructed according to known node coordinate and element number in part；Further using APDL language will be known
External applied load, the elasticity modulus of material, Poisson's ratio, virtual rigidity parameter are written as program code；
Step 3: it is non-thread to call finite element analysis software to carry out to update design parameter using numerical value software for calculation MATLAB
Property finite element solving, obtain compliant mechanism geometrical non-linearity displacement；
Step 4: being displaced using the geometrical non-linearity that step 3 obtains, the structure sensitivity of calculating compliant mechanism topological optimization,
The shared strain energy function C of volume fraction and mechanism；
Step 5: the unit puppet density x ' after solving compliant mechanism topological optimization using Method of Optimality Criteriai, while updating should
Design variable, the design variable x ' solved using this stepiThe x used as next iterationi+1；
Step 6: whether the density in judgment step five meets condition of convergence max (x 'i-xi)<0.001&&loop>100,
I.e. variable density is less than threshold value 0.001 or has reached 100 step of greatest iteration step number twice for front and back, wherein x 'iIt changes for the last time
The design variable in generation, xiFor the design variable of current iteration；Continue iteration if being unsatisfactory for the condition of convergence, stops following if meeting
Ring obtains topologies.
A further technical solution of the present invention is: the topological optimization model is that solid isotropic material punishes model
SIMP。
Beneficial effect
The beneficial effects of the present invention are: it is proposed by the present invention it is a kind of combined based on MATLAB with the compliant mechanism of APDL open up
Optimization method is flutterred, gives complicated non linear finite element analysis part to professional finite element analysis software to complete, and by numerical value
Calculating section gives professional numerical software to calculate.The advantages of learning from other's strong points to offset one's weaknesses, each software is utilized to greatest extent, greatly mentions
High computational efficiency, reduces programming difficulty, while ensure that the precision of solution.The present invention have it is versatile, easy to operate,
The advantages that computational efficiency is high.
Detailed description of the invention
Fig. 1 is the structural schematic diagrams such as design domain, boundary condition, the load of flexible retainer according to the present invention；
Fig. 2 is the scale diagrams of the design domain of flexible retainer according to the present invention；
Fig. 3 is the joint topological optimization result schematic diagram of flexible retainer according to the present invention；
Fig. 4 is the joint topological optimization load deflection figure of flexible retainer according to the present invention.
Specific embodiment
The embodiments described below with reference to the accompanying drawings are exemplary, it is intended to be used to explain the present invention, and cannot understand
For limitation of the present invention.
The present invention is a kind of Topology Optimization Method combined with the compliant mechanism of APDL based on MATLAB the following steps are included:
Step 1 establishes the topological optimization model of compliant mechanism.This method punishes model using solid isotropic material
(SIMP) it is used as topological optimization model.The objective optimization region known to designing given primary condition, is defined as design domain
Φ is discrete for n finite elements by region Φ using finite element analysis software ANSYS.After discrete, by discrete information (unit
Number, node coordinate) export, and define xiFor the corresponding pseudo- density of i-th of discrete unit, viFor the body of i-th of discrete unit
Product, and with unit puppet density xiAs design variable.According to design requirement, the volume constraint score f of given design.With mechanism
The shared minimum objective function of strain energy, constraint condition are that the usage amount of material is less than volume upper limitThe objective function of optimization
It is as follows, wherein u is motion vector, and F is external applied load vector, and R is global Unbalanced force vector, and C is the shared strain of outgoing mechanism
It can function.
S.t.R (u, x)=0
0<xmin≤xi≤ 1, i=1,2 ..., n
Step 2 establishes the finite element analysis model of compliant mechanism.By the discrete letter of design domain Φ obtained in step 1
Breath is handled, will be discrete after element number and node coordinate correspond, and write using parametric programming language APDL
It is after discrete as a result, constructing finite element analysis model according to known node coordinate and element number in ANSYS.Continue to make
Known external applied load, the elasticity modulus of material, Poisson's ratio, virtual rigidity parameter are written as program code with APDL language.?
" NLGEOM, 1 " order, opening large deformation geometrical non-linearity solver switch are added in program code.
Step 3, executed in numerical value software for calculation MATLAB order "！ANSYS170-b-p ane3fl-i-o " is called
ANSYS carries out nonlinear finite element solution, obtains the geometrical non-linearity displacement of compliant mechanism.Wherein " 170 " refer to ANSYS editions
This be 17.0, should be the parametrization APDL language program code worked out in step 2 after "-i ", should be after "-o " call ANSYS into
Output file after the solution of row nonlinear finite element.
Step 4 is displaced using the geometrical non-linearity that step 3 obtains, the structure sensitivity of calculating compliant mechanism topological optimization,
Volume fraction and objective function (shared strain energy C)；
Step 5, the unit puppet density x after compliant mechanism topological optimization is solved using Method of Optimality Criteria (OC)i, while more
The new design variable, uses for next iteration；
Whether step 6, the density in judgment step five meet condition of convergence max (x 'i-xi)<0.001&&loop>100,
I.e. variable density is less than threshold value 0.001 or has reached 100 step of greatest iteration step number twice for front and back.Wherein x 'iIt changes for the last time
The design variable in generation, xiFor the design variable of current iteration.Continue iteration if being unsatisfactory for, is opened up if meeting and stopping circulation
Flutter result.
Specific embodiment refering to fig. 1~Fig. 4, the present invention carries out joint topology optimization design by taking flexible retainer as an example, has
Steps are as follows for body:
Step 1 establishes the topological optimization model of flexible retainer.The design domain that Fig. 1 is flexible retainer is defined, wherein
Left end is external force input point, is two displacement output points at right-end openings, and it is virtual to simulate that spring is added at the place of outputting and inputting
Rigidity.As shown in Fig. 2, design domain is a 60 × 60mm2Square, on the left side, midpoint opens a 12 × 12mm2Pros
V notch v.Initial designs condition is elastic modulus E=100MPa, Poisson's ratio nu=0.3, external force F=5N, inputs stiffness Kin=
0.5N/m exports stiffness Kout=0.1N/m.It defines optimization problem: objective function is up to the output point displacement of clamper, if
Meter variable is unit puppet density xi, constraint condition is that the usage amount of material is less than volume upper limit, wherein volume constraint f=0.3,
SIMP density of material penalty coefficient p=3；
Step 2 establishes the finite element analysis model of flexible retainer.It is set using the discrete clamper of finite element analysis software
Domain Φ is counted, discrete to use 4 Node Quadrilateral Element grids (plane182), size of mesh opening is set as 1 × 1mm2, design domain is separated into
3456 units.Element number and node coordinate after will be discrete correspond, and are write using parametric programming language APDL
It is after discrete as a result, continue to use APDL language by the elasticity modulus of external applied load, material in step 1, Poisson's ratio, it is virtual just
The parameters such as degree are written as program code." NLGEOM, 1 " order are opened large deformation geometrical non-linearity and are asked for addition in program code
Solve device switch.
Step 3 calls ANSYS to carry out nonlinear finite element solution, obtains flexible folder using numerical value software for calculation MATLAB
The geometrical non-linearity of holder is displaced；
Step 4 is displaced using the geometrical non-linearity that step 3 obtains, the structure sensitivity of calculating compliant mechanism topological optimization,
Volume fraction and objective function (output point displacement), and sensitivity is filtered；
Step 5, the cell density x after flexible retainer topological optimization is solved using Method of Optimality Criteria (OC)i(i=1,
2 ..., 3456), and design variable is updated；
Whether step 6, the density in judgment step five meet the condition of convergence, max (x 'i-xi)<0.001&&loop>100,
x′iFor the design variable of previous step iteration, continue iteration if being unsatisfactory for, obtains topologies if meeting and stopping circulation, repeatedly
It is as shown in Figure 3, Figure 4 for result.
Although the embodiments of the present invention has been shown and described above, it is to be understood that above-described embodiment is example
Property, it is not considered as limiting the invention, those skilled in the art are not departing from the principle of the present invention and objective
In the case where can make changes, modifications, alterations, and variations to the above described embodiments within the scope of the invention.
Claims (2)
1. a kind of combine Topology Optimization Method with the compliant mechanism of APDL based on MATLAB, it is characterised in that the following steps are included:
Step 1: the topological optimization model of compliant mechanism is established；Known target optimization region is defined as design domain Φ, using having
Finite element analysis software is discrete for n finite elements by design domain Φ；Information after discrete includes element number and node coordinate, is incited somebody to action
The element number and node coordinate export, and define xiFor the corresponding pseudo- density of i-th of discrete unit, viFor i-th of discrete list
The volume of member, with unit puppet density xiAs design variable；
With the minimum objective function of shared strain energy of the compliant mechanism, constraint condition is that the usage amount of material is less than in volume
LimitThe objective function of optimization is as follows:
S.t.R (u, x)=0
0<xmin≤xi≤ 1, i=1,2 ..., n
Wherein, f is volume constraint score；The volume of V=1, V expression design domain Φ；In the constraint for indicating design domain Φ volume
Limit；U is motion vector, and F is external applied load vector, FTFor the transposition of external applied load vector, R is global Unbalanced force vector, and C is to indicate
The shared strain energy function of mechanism；
Step 2: the finite element analysis model of compliant mechanism is established；The element number and node after will be discrete in step 1
Coordinate correspond, and using parametric programming language APDL write it is discrete after as a result, realize in finite element analysis software
Finite element analysis model is constructed according to known node coordinate and element number；APDL language is further used by known outer load
Lotus, the elasticity modulus of material, Poisson's ratio, virtual rigidity parameter are written as program code；
Step 3: design parameter is updated using numerical value software for calculation MATLAB to call finite element analysis software progress is non-linear to have
Limit member solves, and obtains the geometrical non-linearity displacement of compliant mechanism；
Step 4: it is displaced using the geometrical non-linearity that step 3 obtains, calculates structure sensitivity, the volume of compliant mechanism topological optimization
The shared strain energy function C of score and mechanism；
Step 5: the unit puppet density x ' after solving compliant mechanism topological optimization using Method of Optimality Criteriai, while updating the design
Variable, the design variable x ' solved using this stepiThe x used as next iterationi+1；
Step 6: whether the density in judgment step five meets condition of convergence max (x 'i-xi)<0.001&&loop>100, i.e., before
Variable density is less than threshold value 0.001 or has reached 100 step of greatest iteration step number twice afterwards, wherein x 'iFor last iteration
Design variable, xiFor the design variable of current iteration；Continue iteration if being unsatisfactory for the condition of convergence, stops recycling if meeting
To topologies.
2. combining Topology Optimization Method with the compliant mechanism of APDL based on MATLAB according to claim 1, it is characterised in that:
The topological optimization model is that solid isotropic material punishes model SIMP.
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Cited By (2)
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| CN111539145A (en) * | 2020-04-22 | 2020-08-14 | 安徽工程大学 | Optimization method of compression molding die for automobile hat rack |
| CN113742981A (en) * | 2021-09-18 | 2021-12-03 | 西南交通大学 | Method for designing and manufacturing robustness of flexible medical clamp |
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